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arXiv · 1302.1835

Counting using Hall Algebras II. Extensions from Quivers

Jiarui Fei
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Abstract

We count the $\mathbb{F}_q$-rational points of GIT quotients of quiver representations with relations. We focus on two types of algebras -- one is one-point extended from a quiver $Q$, and the other is the Dynkin $A_2$ tensored with $Q$. For both, we obtain explicit formulas. We study when they are polynomial-count. We follow the similar line as in the first paper but algebraic manipulations in Hall algebra will be replaced by corresponding geometric constructions.

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Jiarui Fei. 2013-02-07. Counting using Hall Algebras II. Extensions from Quivers. https://arxiv.org/abs/1302.1835

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